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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Indecomposable continua and the Julia sets of polynomials


Authors: John C. Mayer and James T. Rogers
Journal: Proc. Amer. Math. Soc. 117 (1993), 795-802
MSC: Primary 58F23; Secondary 30C10, 30D05, 54F15, 54H20
MathSciNet review: 1145423
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Abstract: We find several necessary and sufficient conditions for the Julia set $ J$ of a polynomial of degree $ d \geqslant 2$ to be an indecomposable continuum. One condition that may be easier to check than others is the following: Suppose $ J$ is connected; then $ J$ is an indecomposable continuum iff the impression of some prime end of the unbounded complementary domain of $ J$ has interior in $ J$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1145423-7
PII: S 0002-9939(1993)1145423-7
Keywords: Julia set, indecomposable continuum, internal composant, prime end, simple dense canal, Lake of Wada, complex analytic dynamics, conformal dynamics
Article copyright: © Copyright 1993 American Mathematical Society